What are the key components of sinusoidal wave equations?

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SUMMARY

The discussion focuses on the key components of sinusoidal wave equations, specifically analyzing the equation y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad). The wavelength (λ) is determined to be 0.524 m, calculated using the formula (2π)/k, where k is the wave number (12.0). The phase difference between the two waves is established through their respective phase shifts, and the amplitude (ym) is confirmed as 5.5 mm. Understanding the equation's structure is crucial for grasping wave behavior.

PREREQUISITES
  • Understanding of sinusoidal wave equations
  • Knowledge of wave properties such as wavelength and amplitude
  • Familiarity with trigonometric identities
  • Basic physics concepts related to wave motion
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  • Study the derivation of the wave equation from basic principles
  • Learn about the relationship between wave number and wavelength
  • Explore trigonometric identities for combining sine functions
  • Investigate the effects of phase shifts on wave interference
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Mr Krabs
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Member advised to use the homework template for posts in the homework sections of PF.
Two sinusoidal waves, identical except for phase, travel in the same direction along a string, producing the net wave

y(x,t)=(5.5 mm)sin(12.0x -2.0 s-1 * t+0.390 rad),


A. with x in meters and t in seconds. What is the wavelength λ of the two waves?
B. What is the phase difference between them?
C. What is their amplitude ym?


I know A is .524 m but I am not too sure why. Other than that, I don't really know what I am doing. My general issue here is that I do not fully understand the form of the equation. Any information on what the different terms in the equation do would be helpful.

I got the answer for A from (2pi)/12 btw. The 12 was the coefficient of the first term, but again I don't really understand what is happening here.
 
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Mr Krabs said:
I know A is .524 m but I am not too sure why.
The wavelength is the smallest nonzero change in x which completes a cycle, i.e. changes the argument to the sine function by 2π.
Mr Krabs said:
I do not fully understand the form of the equation.
Write a general equation for a traveling wave. Write a second one which only differs in phase. Write the sum of the two.
What trig formulae do you know that can put the sum of two sine functions in a different form? (These should be listed in the Relevant Equations section of the template. Oh, you didn't keep the template. Tut tut.)
 

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